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sampletest11(2)

# sampletest11(2) - Math 137 Sample problems for Test I 1 The...

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Math 137 Sample problems for Test I 1. The vector a starts from the point (1 , 1 , 1) and end at (2 , 2 , 2) . The vector b starts from the point (1 , 2 , 3) and end at (2 , 3 , 4). Find a . Are vectors a and b different? 2. Given a = (1 , 1 , 2) and b = (2 , 3 , 4), find a · b and a × b . 3. The equations for two straight lines are x 1 = y 2 = z 3 and x 1 = y 1 = z - 1 respectively. Do these two lines pass the point (0 , 0 , 0)? Are they perpendicular to each other? 4. A plane contains three points: (0 , 0 , 0), (1 , 1 , 1) and (3 , 2 , 1). (a) Find an equation for the plane. (b) Find the area of the triangle with these three points as its vertices. (c) Find a parametric equation for the line PERPENDICULAR TO THE PLANE and passing through the point (1 , 2 , 3). (d) Find the point P where the line in (c) passing through the plane. (e) Find the distance between the point (1 , 2 , 3) to the plane, using the following two methods: The first one is to use the result in (c) and (d). The other is to use the formula in the textbook.

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sampletest11(2) - Math 137 Sample problems for Test I 1 The...

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